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ENERGY                                      201
1.  What should be the tractive force of a locomotive in order that ii may be able to give a train of 150 tons a velocity of 45 miles per hour within one mile from the start?   The resistance per ton is given in pounds bj the numerical relation R = 5 + 0.4 v2, where v is the velocity in miles pei hour.
2.   In the preceding problem find the limiting velocity.
3.  The effective horse power of a vertical water wheel is 46 and its efficiency is 70 per cent.    If the head of water is 25 feet find the numbe] of gallons of water which have to be delivered to the wheel per minute.
4.   A belt running at a speed of 1500 feet per minute transmits 25 hors< power.   Assuming the tensile force on the tight side of the belt to b< twice that on the slack side, find both tensile forces.
5.   In the preceding problem find the width of the belt if the saf< tensile force is 75 pounds per inch width of the belt.
6.   Find the power which may be transmitted by a belt under th following conditions:
The width of the belt is 10 inches.
The pulley which the belt drives is 4 feet in diameter and make;
125 revolutions per minute.
The arc of contact subtends an angle of 150 at the center. The coefficient of friction is 0.4. The tensile force of the belt is not to exceed 90 pounds per inc"
of width.
7.   In the preceding problem find the tensile force on the slack sid of the belt.
8.   In problem 6 suppose the arc of contact to subtend 120 at th center of the pulley.
9.   In the preceding problem find the tensile force per inch width c the belt on the slack side.
10.   Find the power lost due to friction in the bearings of a flywhe* under the following conditions:
The journals are 6 inches in diameter and 10 inches long.
The coefficient of friction is 0.004.
The flywheel weighs 15 tons and makes 200 revolutions pe
minute. The normal pressure on the bearings is constant over the surfac
of contact.
11.   In the preceding problem suppose the vertical component of th total reaction to be constant.